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Article type: Research Article
Authors: García-Melián, Jorge; | Rossi, Julio D.; | Sabina de Lis, José C.;
Affiliations: Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain. E-mails: jjgarmel@ull.es, josabina@ull.es | Instituto Universitario de Estudios Avanzados en Física Atomica, Molecular y Fotonica, Facultad de Física, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38203 La Laguna, Spain | Departamento de Análisis Matemático, Universidad de Alicante, Ap. correos 99, 03080 Alicante, Spain. E-mail: jrossi@dm.uba.ar
Note: [] On leave from Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1, (1428), Buenos Aires, Argentina.
Abstract: In this work we discuss existence, uniqueness and asymptotic profiles of positive solutions to the quasilinear problem −Δpu+a(x)up−1=−ur in Ω, |∇u|p−2 ∂u/∂ν=λup−1 on ∂Ω for λ∈R, where r>p−1>0, a∈L∞(Ω). We analyze the existence of solutions in terms of a principal eigenvalue, and determine their asymptotic behavior both when r→p−1 and when r→∞.
Keywords: linear and nonlinear eigenvalue problems, sub- and super-solutions, variational methods
DOI: 10.3233/ASY-2011-1035
Journal: Asymptotic Analysis, vol. 73, no. 3, pp. 147-168, 2011
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